MCAT Physics Equation Sheet

8/10/2019 MCAT Physics Equation Sheet

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2011 The College Board. Visit the College Board on the Web: www.collegeboard.org.

Table of Information and Equation Tables for AP Physics Exams

The accompanying Table of Information and Equation Tables will be provided to students when

they take the AP Physics Exams. Therefore, students may NOT bring their own copies of thesetables to the exam room, although they may use them throughout the year in their classes in

order to become familiar with their content. Check the Physics course home pages on AP

Central for the latest versions of these tables (apcentral.collegeboard.).

Table of Information

For both the Physics B and Physics C Exams, the Table of Information is printed near the front

cover of the multiple-choice section and on the green insert provided with the free-response

section. The tables are identical for both exams except for one convention as noted.

Equation Tables

For both the Physics B and Physics C Exams, the equation tables for each exam are printed onlyon the green insert provided with the free-response section. The equation tables may be used by

students when taking the free-response sections of both exams but NOT when taking the

multiple-choice sections.

The equations in the tables express the relationships that are encountered most frequently in

AP Physics courses and exams. However, the tables do not include all equations that might

possibly be used. For example, they do not include many equations that can be derived by

combining other equations in the tables. Nor do they include equations that are simply special

cases of any that are in the tables. Students are responsible for understanding the physical

principles that underlie each equation and for knowing the conditions for which each equation is

applicable.

The equation tables are grouped in sections according to the major content category in whichthey appear. Within each section, the symbols used for the variables in that section are defined.

However, in some cases the same symbol is used to represent different quantities in different

tables. It should be noted that there is no uniform convention among textbooks for the symbols

used in writing equations. The equation tables follow many common conventions, but in some

cases consistency was sacrificed for the sake of clarity.

Some explanations about notation used in the equation tables:

1. The symbols used for physical constants are the same as those in the Table of

Information and are defined in the Table of Information rather than in the right-hand

columns of the tables.

2. Symbols in bold face represent vector quantities.

3.

Subscripts on symbols in the equations are used to represent special cases of thevariables defined in the right-hand columns.

4. The symbol before a variable in an equation specifically indicates a change in the

variable (i.e., final value minus initial value).

5.

Several different symbols (e.g., d, r, s, h, ) are used for linear dimensions such as

length. The particular symbol used in an equation is one that is commonly used for

that equation in textbooks.


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TABLE OF INFORMATION DEVELOPED FOR 2012 (see note on cover page)

CONSTANTS AND CONVERSION FACTORS

Proton mass,271.67 10 kgpm

Electron charge magnitude, 191.60 10 Ce

Neutron mass, 271.67 10 kgnm 1 electron volt, 191 eV 1.60 10 J

Electron mass, 319.11 10 kgem Speed of light, 83.00 10 m sc

Avogadros number,23 -1

0 6.02 10 molN Universal gravitational

constant,11 3 2

6.67 10 m kg sG

Universal gas constant, 8.31 J (mol K)R Acceleration due to gravityat Earths surface,

29.8 m sg

Boltzmanns constant, 231.38 10 J KBk

1 unified atomic mass unit, 27 21 u 1.66 10 kg 931 MeV c

Plancks constant, 34 156.63 10 J s 4.14 10 eV sh

25 31.99 10 J m 1.24 10 eV nmhc Vacuum permittivity, 12 2 20 8.85 10 C N m

Coulombs law constant, 9 201 4 9.0 10 N m Ck 2

Vacuum permeability, 70 4 10 (T m) A

Magnetic constant, 70 4 1 10 (T m)k A

1 atmosphere pressure, 5 2 51 atm 1.0 10 N m 1.0 10 Pa

meter, m mole, mol watt, W farad, F

kilogram, kg hertz, Hz coulomb, C tesla, T

second, s newton, N volt, V degree Celsius, C ampere, A pascal, Pa ohm, electron-volt, eV

UNITSYMBOLS

kelvin, K joule, J henry, H

PREFIXES VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES

0

30

37

45

53

60

90Factor Prefix Symbol

910 giga G 3 5 2 2 3 21 2 4 5sin 10

4 5610 mega M 3 2 2 2 1 23 5cos 01

310 kilo k 3 4 3 3 4 3tan 0 1 3 2

10

centi cThe following conventions are used in this exam.

310

milli m I. Unless otherwise stated, the frame of reference of any problem is

assumed to be inertial.610

micro

II. The direction of any electric current is the direction of flow of positivecharge (conventional current).

910

nano n

1210

pico p III. For any isolated electric charge, the electric potential is defined as zero at

an infinite distance from the charge.*IV. For mechanics and thermodynamics equations,Wrepresents the work

done on

a system.

*Not on the Table of Information for Physics C, since Thermodynamics is not aPhysics C topic.


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ADVANCED PLACEMENT PHYSICS B EQUATIONS DEVELOPED FOR 2012

MECHANICS

ELECTRICITY AND MAGNETISM

2

1 2

0 a = acceleration A = area

F = force B = magnetic field2

0 01

2

0

f = frequency C = capacitance

FE h = height d = distance

2 20 2 J = impulse E = electric field1 2

= emfK = kinetic energyk = spring constant F = force

F F a

= length I = current m = mass

2

sin F

p v

J F p

21

2

cos

cos

F x

21

2

2

2

1

1 2

2

1 2

N = normal force

P = power

p = momentum

r = radius or distance

T = period

t = time

U = potential energy

= velocity or speed

W = work done on

a system

x = position

= coefficient of friction

= angle

= torque

31 2

1 2 3

...

= length

P = power

Q = charge

q = point charge

R = resistancer = distance

0

t = time

U = potential (stored)

energy21 1

2 2

= electric potential or

potential differenc

= velocity or speed

1 2 3 ...

1 2 3

1 1 1 1...

1 2 3 ...

1 2 3

1 1 1 1...

sin

sin

02

cos

avg

= resistivity

= angle

= magnetic flux


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ADVANCED PLACEMENT PHYSICS B EQUATIONS DEVELOPED FOR 2012

FLUID MECHANICS AND THERMAL PHYSICS WAVES AND OPTICS

m V A = area d = separationf = frequency ore = efficiency

0 focal lengthF =force

1 1 2 2

21 const.2

0

3

2

33

h =depth

H =rate of heat transfer

k =thermal conductivity

= average molecular

kinetic energy

= length

L =thickness

m = mass

M = molar mass

n = number of moles

N = number of molecules

P = pressure

Q = heat transferred to a

systemT = temperature

U = internal energy

=volume

=velocity or speed

= root-mean-square

velocity

W = work done on a system

y =height

= coefficient of linearexpansion

= mass of molecule =density

1 1 2sin sin 2h = height

L = distance

M = magnification2

1

sin

m = an integer

n = index of

0

1 1 1

refractionR = radius of

curvature

0 0

s = distance

= speed

x = position

2

= wavelength

= anglesin

GEOMETRY AND TRIGONOMETRY

Rectangle

Triangle

1

2

Circle2

2

Rectangular Solid

Cylinder

2

22 2

ATOMIC AND NUCLEAR PHYSICS

Sphere

34

3

max

2( )

E = energy

f = frequencyK = kinetic energy

= mass

p = momentum

= wavelength

= work function

24

2

Right Triangle

2 2

sin

cos

ta

n

A = area

C = circumference

V = volume

S = surface area

b = base

h= height

= length

w = width

r = radius

ca

b

90q


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ADVANCED PLACEMENT PHYSICS C EQUATIONS DEVELOPED FOR 2012

MECHANICS

ELECTRICITY AND MAGNETISM

2

1 2

0

1

4

0 a = acceleration A = area

F = force B = magnetic field2

0 01

2

0

f = frequency C = capacitance

FE h = height d = distance

I = rotational inertia E = electric field2 20 2 = emfJ = impulse

0

E A

K = kinetic energy F = force F F a

k = spring constant I = current

pF

= length J = current density

L = angular momentum L = inductance

m = mass = length

0

1

4

J F p N = normal force n = number of loops of wireper unit lengthP = power

p v N = number of charge carrier per unit volume

p = momentum1 2

0

1

4

r = radius or distance

P = powerr = position vectorQ = charge

T = period F r q = point charget = timeR = resistanceU = potential energy

21

2 0

r = distance = velocity or speedt = timeW = work done on a systemU = potential or stored energy

x = position= electric potentia= coefficient of friction = velocity or speed= angle 1 1

F v = resistivity = torque

= magnetic flux

= angular speed

= dielectric constant = angular acceleration

22

= phase angle

21 1

2 2

0B F x r F

2 2

r r

L r p

21

2

0

20 0

1

2

21

2

0

34

rB

max cos(x x t E J F B 2 1

0

B A

E

21

2

2

2

1 2

2

F r

1 1

F v B 1 2


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ADVANCED PLACEMENT PHYSICS C EQUATIONS DEVELOPED FOR 2012

GEOMETRY AND TRIGONOMETRY CALCULUS

Rectangle A = area

C = circumference V = volume

TriangleS = surface area

12

b = baseh = height

= lengthCircle

w = width2 r = radius

2 Rectangular Solid

Cylinder

2

22 2

Sphere

34

3

24

Right Triangle

2 2 2

sin

cos

tan

ca

b

90q

1

1

ln

sin cos

cos sin

11 , 1

1

ln

cos sin sin cos

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MCAT Physics Equation Sheet